SOLUTION OF THE INCOMPRESSIBLE LAMINAR BOUNDARY-LAYER EQUATIONS

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Abstract

A general method is presented for calculation of the incompressible steady laminar boundary layer around either a two-dimensional or an axially symmetric body. The method is a modification of the Hartree-Womersley method. It consists of replacing the partial derivatives with respect to the flow direction by finite differences, while retaining the derivatives in a direction normal to the boundary, so that the partial differential equation becomes approximated by an ordinary differential equation. Reasons for choosing this method rather than the more conventional finite-difference methods are discussed. The method has been programed for an electronic computer, and solutions for a variety of flows are presented. Comparisons are made with other exact and approximate methods of solution. They include cases of flow separation, mass transfer, and discontinuities in the boundary conditions. A study of the response of the boundary layer to local boundary conditions is presented. Some comparison with experimental measurement is made also. The large number of calculations and comparisons establish that the method is rapid, accurate, and powerful. It appears capable of solving any flow problem for which the boundary-layer equations themselves remain valid. The only exception is a flow with a discontinuity in a boundary condition, where the method cannot produce an answer immediately downstream of the discontinuity but does appear to be precise a short distance farther downstream.

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